Multidimensional Mechanism Design via AI-Driven Approaches

This chapter explores the application of our AI-driven mechanism design framework to achieve optimal mechanisms for multidimensional auctions. Previous approaches to designing revenue-optimal auctions in these contexts often result in non-truthful or suboptimal mechanisms and are typically limited to specific settings. In this chapter, we implement our framework by concatenating two neural networks: One generates the mechanism, while the other determines actions for the buyers. This separation in design mitigates the challenge of imposing incentive compatibility constraints on the mechanism by utilizing an indirect mechanism. Consequently, our framework effectively addresses the difficulty of incorporating IC constraints, consistently yielding exactly incentive-compatible mechanisms. We also apply our framework to several multi-item auction design settings, including some where the theoretically optimal mechanisms remain unknown. Finally, we provide a theoretical proof that the mechanisms identified by our framework are indeed optimal. To the best of our knowledge, our framework is the first to use neural networks to discover auction mechanisms that are provably optimal.